Solution 1.3:4c
From Förberedande kurs i matematik 1
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- | The whole expression consists of factors having a base of | + | The whole expression consists of factors having a base of 5 so the power rules can be used to simplify the expression first |
- | + | ||
- | + | {{Displayed math||<math>\begin{align} | |
- | + | \frac{5^{12}}{5^{-4}}\cdot \bigl( 5^{2} \bigr)^{-6} | |
- | + | &= \frac{5^{12}}{5^{-4}}\cdot 5^{2\cdot (-6)}\\[3pt] | |
- | + | &= \frac{5^{12}}{5^{-4}}\cdot 5^{-12}\\[3pt] | |
- | <math>\begin{align} | + | &= \frac{5^{12}\cdot 5^{-12}}{5^{-4}}\\[3pt] |
- | + | &= \frac{5^{12-12}}{5^{-4}}\\[3pt] | |
- | + | &= \frac{5^{0}}{5^{-4}}\\[3pt] | |
- | & =\frac{5^{12-12}}{5^{-4}}=\frac{5^{0}}{5^{-4}}=5^{0- | + | &= 5^{0-(-4)}\\[3pt] |
- | \end{align}</math> | + | &= 5^{4}\\[3pt] |
+ | &= 5\cdot 5\cdot 5\cdot 5\\[3pt] | ||
+ | &= 625\,\textrm{.} | ||
+ | \end{align}</math>}} |
Current revision
The whole expression consists of factors having a base of 5 so the power rules can be used to simplify the expression first
\displaystyle \begin{align}
\frac{5^{12}}{5^{-4}}\cdot \bigl( 5^{2} \bigr)^{-6} &= \frac{5^{12}}{5^{-4}}\cdot 5^{2\cdot (-6)}\\[3pt] &= \frac{5^{12}}{5^{-4}}\cdot 5^{-12}\\[3pt] &= \frac{5^{12}\cdot 5^{-12}}{5^{-4}}\\[3pt] &= \frac{5^{12-12}}{5^{-4}}\\[3pt] &= \frac{5^{0}}{5^{-4}}\\[3pt] &= 5^{0-(-4)}\\[3pt] &= 5^{4}\\[3pt] &= 5\cdot 5\cdot 5\cdot 5\\[3pt] &= 625\,\textrm{.} \end{align} |